A. 2023
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

In a sequence $$$a$$$, whose product was equal to $$$2023$$$, $$$k$$$ numbers were removed, leaving a sequence $$$b$$$ of length $$$n$$$. Given the resulting sequence $$$b$$$, find any suitable sequence $$$a$$$ and output which $$$k$$$ elements were removed from it, or state that such a sequence could not have existed.

Notice that you are not guaranteed that such array exists.

Input

Each test consists of several test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. This is followed by a description of the test cases.

The first line of each test case contains two integers $$$n$$$ ($$$1 \le n, k \le 5$$$) — the size of sequence $$$b$$$ and the number of numbers removed from sequence $$$a$$$.

The second line contains $$$n$$$ integers $$$b_1,b_2, \ldots,b_n$$$ ($$$1 \leq b_i \leq 2023$$$) — the remaining sequence. The values of $$$b_i$$$ might not be divisors of $$$2023$$$.

Output

For each test case, output "YES" if the sequence $$$a$$$ exists, and in the following line output $$$k$$$ non-negative integers that were removed from the sequence $$$a$$$. If the sequence $$$a$$$ does not exist, output "NO" in a single line.

You can output the answer in any case (uppercase or lowercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive answers.

Example
Input
7
2 2
5 2
3 1
7 17 7
4 2
1 289 1 1
3 1
7 17 17
1 1
289
1 1
2023
1 3
1
Output
NO
NO
YES
7 1
YES
1
YES
7
YES
1
YES
7 17 17
Note

In third test case product is equal to $$$289 \cdot 7 = 2023$$$.

In fourth test case product is already equal to $$$2023$$$.

In seventh test case product is equal to $$$7 \cdot 17 \cdot 17 = 2023$$$.